Pseudo-polynomial functions over finite distributive lattices

TL;DR

This paper introduces and characterizes pseudo-polynomial functions over finite distributive lattices, providing axioms and tools for their factorization, expanding understanding of aggregation models in lattice-based systems.

Contribution

It offers a new axiomatization for pseudo-polynomial functions and develops methods to find all factorizations of such functions over finite distributive lattices.

Findings

A new axiomatization for pseudo-polynomial functions.

General tools for factorization of these functions.

Complete characterization of factorizations.

Abstract

In this paper we consider an aggregation model f: X1 x ... x Xn --> Y for arbitrary sets X1, ..., Xn and a finite distributive lattice Y, factorizable as f(x1, ..., xn) = p(u1(x1), ..., un(xn)), where p is an n-variable lattice polynomial function over Y, and each uk is a map from Xk to Y. The resulting functions are referred to as pseudo-polynomial functions. We present an axiomatization for this class of pseudo-polynomial functions which differs from the previous ones both in flavour and nature, and develop general tools which are then used to obtain all possible such factorizations of a given pseudo-polynomial function.